基于振动频谱的特征提取与选择在球磨机负荷参数估算中的应用研究

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基于振动谱的特征提取与选择及其在磨削过程中球磨机负荷参数估算中的应用本文主要讨论基于振动谱的特征提取与选择方法，并应用于磨削过程中球磨机负荷参数的估算。振动谱是一种常用的信号处理方法，通过对振动信号的频谱分析，可以提取出有价值的特征信息。对于磨削过程中的球磨机负荷参数估算，传统的方法通常需要安装传感器以获取磨削过程中的实时数据，但是这需要较高的成本和复杂的安装过程。本文提出的基于振动谱的特征提取与选择方法可以克服传统方法的缺陷。该方法首先对磨削过程中的振动信号进行频谱分析，以提取出频谱特征。然后，对这些特征进行选择，以便更好地描述磨削过程中的负荷参数。该方法可以实时地获取磨削过程中的负荷参数，无需安装传感器，从而降低了成本和提高了效率。在本文中，我们首先介绍了基于振动谱的特征提取方法，包括时域分析、频域分析和时频域分析等。然后，我们讨论了特征选择方法，包括 filter 方法、wrapper 方法和embedded 方法等。最后，我们将该方法应用于磨削过程中球磨机负荷参数的估算，并对结果进行了分析和讨论。本文的贡献在于提出了一种基于振动谱的特征提取与选择方法，并将其应用于磨削过程中球磨机负荷参数的估算。该方法可以实时地获取磨削过程中的负荷参数，无需安装传感器，从而降低了成本和提高了效率。 knowledge points: 1. 振动谱是一种常用的信号处理方法，可以用于提取有价值的特征信息。 2. 基于振动谱的特征提取方法可以用于磨削过程中球磨机负荷参数的估算。 3. 特征选择方法可以用于选择最有价值的特征，以便更好地描述磨削过程中的负荷参数。 4. 基于振动谱的特征提取与选择方法可以实时地获取磨削过程中的负荷参数，无需安装传感器。 5. 该方法可以降低成本和提高效率。关键词：振动谱、特征提取、特征选择、磨削过程、球磨机负荷参数估算。资源链接： * 《基于振动谱的特征提取与选择及其在磨削过程中球磨机负荷参数估算中的应用》论文 * 《振动谱分析》书籍 * 《信号处理》书籍 * 《磨削过程控制》书籍

features overcome the disadvantages of the feature selection and

extraction method for vibration spectrum modeling. However, the

obtained features contain redundancy and complement informa-

tion. Thus, the AGA is applied in LS-SVM to reselect the input sub-

set from the candidate features and the LS-SVM parameters

simultaneously. Thus, the proposed method integrates feature

selection, extraction and modeling. It has been successfully

applied in a laboratory-scale wet ball mill.

The remaining part of the paper is organized as follows.

Section 2 describes the scheme of the proposed feature extraction

and selection method using the vibration frequency spectrum.

Section 3 gives the realization of the proposed method. Section 4

gives the application research results. The conclusions of the

paper are given in Section 5.

2. Scheme of the feature extraction and selection using

vibration frequency spectrum

By using the Fourier transform, the frequency spectrum

becomes a complex. It describes the magnitude and phase of

the mill shell vibration signal. In mill load modeling, phase

information is not important. By discarding the phase informa-

tion, it is possible to simplify the information in a frequency-

domain representation to generate a frequency spectrum or

spectral density. Therefore, based on the analysis of the previous

sections, a feature selection and feature extraction method using

vibration frequency spectrum is proposed to estimate the ML

parameters. The approach consists of local peak features selection

based on MI, spectral segment features extraction based on

clustering and PCA/KPCA, frequency sub-bands selection based

on the MI, and combinational optimization based on AGA.

The strategy diagram is illustrated in Fig. 1.

In Fig. 1, superscript t and f represent the time domain and

frequency domain respectively; subscript v represents shell

vibration; x

is the original time domain signal; x

represents

the vibration frequency spectrum; x

represents the spectral

segment, d ¼ 1, ..., D

, D

is the number of the vibration spectral

segments; z

peak

is the local peaks features; z

selpeak

is the local peaks

features for the ith ML parameter selected with MI algorithm; z

sub

is the characteristic frequency sub-bands; z

selsub

is the frequency

sub-bands for the ith ML parameter selected with MI algorithm;

extr

is the extracted features of the spectral segments for the ith

ML parameter with PCA/KPCA algorithm; z

¼½z

selpeak

, z

extr

, z

selsub



represents the candidate features for the ith ML parameter;

and

represent the candidate parameters of the soft sensor

model;

and z

sel

represent the selected models’ parameters

and the input sub-set for the ith ML parameter using AGA based

combinational optimization algorithm; y

and

represent the real

and the estimate of the ith ML parameter and i¼1, 2 and 3

represent MVBR, PD and CVR respectively.

Fig. 4 shows that the input and output of the soft sensor model

are x

and y

respectively. The functions of different modules are

shown as follows:

(1) Local peak feature selection based on MI: calculate the features

of the local peaks and select different features using MI-based

feature selection method for different ML parameters.

(2) Spectral segment feature extraction based on clustering and

PCA/KPCA: partition the spectrum into several segments

automatically using the modiﬁed spectral segment clustering

algorithm, and extract the linear and nonlinear features of

different spectral segments using PCA/KPCA algorithm.

(3) Frequency sub-band selection based on the MI: select characteristic

frequency sub-bands using MI based feature selection method for

different ML parameters.

(4) Combinational optimization based on AGA: combine these

features as the candidate features and select the input sub-

set and parameters of the soft sensor models simultaneously

using AGA algorithm, which is called combinatorial optimiza-

tion in this paper. There are several reasons to carry out the

combinatorial optimization: (1) the information of ML para-

meters in different features are complementary and redun-

dant; (2) each ML parameter has its own features; (3) for the

same input sub-set, the optimized model parameters can

improve the prediction performance; and (4) the input sub-

set and the model parameters inﬂuence each other.

The spectral segmentation is a standard approach used in

many modeling exercises. This paper discusses the vibration

frequency spectrum. The vibration frequency spectrum has the

following properties: the vibration spectrum consists of at least

two spectral segments, one is the vibration mode caused by the

ball mill shell and load inside the mill, another one is caused by

the cyclical impaction of the ball load to mill shell. To deal with

the above properties, some special spectral segmentation meth-

ods are needed. Studies show different spectral segments contain

different ML information. The vibration spectrum consists of lots

of local peaks which can be clustered into several segments.

Each segment has different physical interpretation. A clustering

Shell vibration

Ball mill

Grinding process

Vibration frequecny spectrum

Candidate features

Soft sensor model

Fresher ore

Fresh water

Recycle pulp

Balls

Disturbs

Experimental design

Adaptive GA

Candidate models’

parameters

peak

Local peaks’

features

Feature

selection

based on MI

selpeak

Local peak features selection

Sepctral

segments

automatic

partition

Feature

extraction

based on

PCA/KPCA

Spectral segment features extration

Characteristic

frequency

sub-bands

Feature

selection

based on MI

Frequency sub-bands selection

...

sub

selsub

extr

sel

Combinatorial optimization

based on AGA

...

peak

Mill load

arameters

Fig. 1. Strategy diagram of the proposed approach.

J. Tang et al. / Control Engineering Practice 20 (2012) 991–1004 993

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